Solve left(x+yright)^2-left(y-xright)^2

$${ \left(x+y \right) }^{ 2 } - { \left(y-x \right) }^{ 2 }$$

Evaluate

$$4xy$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.

$$x^{2}+2xy+y^{2}-\left(y-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-x\right)^{2}.

$$x^{2}+2xy+y^{2}-\left(y^{2}-2yx+x^{2}\right)$$

To find the opposite of y^{2}-2yx+x^{2}, find the opposite of each term.

$$x^{2}+2xy+y^{2}-y^{2}+2yx-x^{2}$$

Combine y^{2} and -y^{2} to get 0.

$$x^{2}+2xy+2yx-x^{2}$$

Combine 2xy and 2yx to get 4xy.

$$x^{2}+4xy-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$4xy$$

Expand

$$4xy$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.

$$x^{2}+2xy+y^{2}-\left(y-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-x\right)^{2}.

$$x^{2}+2xy+y^{2}-\left(y^{2}-2yx+x^{2}\right)$$

To find the opposite of y^{2}-2yx+x^{2}, find the opposite of each term.

$$x^{2}+2xy+y^{2}-y^{2}+2yx-x^{2}$$

Combine y^{2} and -y^{2} to get 0.

$$x^{2}+2xy+2yx-x^{2}$$

Combine 2xy and 2yx to get 4xy.

$$x^{2}+4xy-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$4xy$$